Detailed Analytical Solution Research Articles

Temperature-assisted electromagnetic surface modes in graphene-based temperature sensitive metafilms

Graphene has the potential to manipulate surface modes in frequency bands from THz to mid-IR regions. Typically, due to single-atom thickness and low charge-carrier density, the thermal response of graphene is ineffective. Temperature-sensitive materials (TSMs) can play an active role in enhancing the thermal response of graphene-based devices. In the present work, graphene-based temperature-sensitive metafilms have been proposed for thermally tunable propagation of electromagnetic surface modes. A detailed analytical and numerical solution for temperature-dependent electromagnetic surface (even and odd) modes supported by the graphene-based temperature-sensitive metafilm has been studied. The Kubo’s formulation has been used to model optical conductivity (σ g ) while the hybrid Drude’s model is implemented to realize the indium antimonide (InSb) as temperature-sensitive material. To simulate the metafilm, the waveguide modal analysis approach was implemented, while the realization of the graphene sheets was achieved by the use of impedance boundary conditions (IBCs). The propagation characteristics for even/odd surface modes were analyzed under different values of temperature (T), chemical potential (µ c ), and thickness of metafilm (d). Further, the numerical results for even and odd surface modes under two phases of InSb [Insulator phase (T = 200 K) and metallic phase (T = 300 K)] were compared under different values of chemical potential (µ c ) and TSM film thickness (d). It is concluded that the propagation characteristics of surface modes are sensitive to the external temperature and can be tailored by tuning the temperature, chemical potential (µ c ), and TSM film thickness (d). Moreover, the degeneracy of the even and odd modes can be controlled by varying the temperature and TSM film thickness. The work is suitable for designing temperature-assisted dual channel waveguides, THz optical switches, THz optical logic designs, and flexible thermal-optical sensors.

Optimization of the Processes of Attenuation of Transverse Movements of a Trailer Following a Tractor

The article considers the issues of optimizing the processes of attenuation of the transverse movements of the trailer, which is attached to a tractor moving at a constant speed with the help of a hinge and taking into account the compliant clutch. As an optimization criterion characterizing the efficiency of this attenuation, the maximization of the degree of system stability is taken. In this case, the distance from the center of mass of the trailer to the point of its adhesion to the tractor acts as an optimized parameter. A detailed analytical solution of the problem is carried out, during which the optimal curve on the plane of dimensionless parameters is determined, which consists of several sections and is located in the region of motion stability. Visual graphic illustrations are given, explaining the meaning of the found solution and its main features. In addition, the obtained results are compared with the variant of the location of the center of mass of the trailer exactly in the middle between the point of its coupling with the tractor and the axle of the wheelset, and an assessment is made of the effectiveness of the obtained optimal solution. The conclusions made in the work are not only of theoretical interest, but can also find some practical application.

Lifting Stokes' paradox by accelerating flow past a circular cylinder and extension of the analysis to the sphere

It is known that Stokes' paradox exhibits in various flow conditions, most notably, in flow past a two-dimensional (2D) circular cylinder. In this study, we provide an example through detailed analytical solution that Stokes' paradox can be lifted by accelerating flow past a stationary cylinder. The analysis is also extended to the case of the accelerating flow past a stationary sphere although in this case, there is no Stokes' paradox. The effects of the acceleration parameter on the flow streamlines, the pressure, and the vorticity distributions, as well as on the drag coefficient, are investigated. The drag comprises the potential component and vorticity component, which are further due to form drag and frictional drag receiving a separate investigation. However, the drag decomposition is also examined the viewpoint of the force decomposition: the total drag = the potential component + surface vorticity component + volume vorticity component.

Role of quantum-coherence dressed states on the Fresnel–Fizeau drag and optical properties of surface plasmon polaritons through asymmetric double quantum dot-metallic plasmonic interfaces

Owing to the exceptional structural-design flexibility and tunability of physical properties of quantum dots, the manipulation of light in view of surface plasmons via dots–based hybrid nanostructures and dots-metallic interfaces finds promising device applications. Hereby, we first demonstrate theoretically the role of intense laser-excited dressed states on the light propagation, optical properties, and lateral and rotary drag of surface plasmon polaritons (SPPs), via plasmon-assisted induced transparency (PIT). For this, we employed a scheme of plasmonic interface comprising an asymmetric double quantum dot molecule GaAs/AlGaAs in the Λ − type configuration embedded in gold metallic surface. In particular, using density-matrix formulation, we present a detailed analytical solution of the quantum dot system for the required eigenvalues in view of the dressed eigenstates. The dressed states played a vital role in the formation of PIT transparency and hence the manipulation of SPPs propagation, optical properties and SPPs drag, via quantum interference. The calculated theoretical results on the optical properties such as absorption and dispersion spectrum, group index, group velocity, group delay, phase delay, wave vector, propagation length and SPPs drag are further elaborated with aid of numerical simulation. The maximum calculated lateral and rotary SPPs drag was of order ± 6.0 × 10−8 m or rad, respectively. The value of SPPs propagation lengths calculated along and perpendicular to the dot-metallic interface are 3.3 × 10−7 m and 2.0 × 10−9 m, respectively.

Role of intense laser-excited dressed states via electromagnetically induced transparency on the Fresnel-Fizeau photon drag through an asymmetric double quantum dot molecule (GaAs/AlGaAs) in the Λ-type configuration

Hereby, we first report theoretical demonstration on the role of intense laser-excited dressed states on the superluminal-assisted propagation, optical properties, and lateral and rotary photon drag, via electromagnetically induced transparency (EIT). For this, we employed a scheme of an asymmetric double quantum dot molecule GaAs/AlGaAs in the Λ − type configuration. In particular, using the compact density-matrix formulism, we present a detailed analytical solution for the required eigenvalues of the system in view of the dressed states. The dressed-states played a vital role on the formation of EIT and hence the modification of dispersion and absorption spectra of the system via quantum interference. The calculated theoretical results on the optical properties such as absorption and dispersion spectrum, group index, group velocity , group delay, phase delay and photon drag are further elaborated with the aid of numerical simulation. Switching ON the control field, the OFF-field single ON-resonance absorption peak split into an OFF-resonance absorption doublet accompanied by an ON-resonance absorption-less dip in the form of EIT window. Interestingly, the absorption doublet split further into an absorption peak and a gain singlet well below and just above the resonance, at a small control field detuning. Further increase in the control-field detuning resulted in a near-resonance gain singlet. Alongside, by tuning various spectral parameters, we observed an interesting switching from luminal to subluminal and superluminal propagation. The optimal calculated values of positive and negative group velocity are 6 × 10 11 m/s and − 2.5 × 10 11 m/s, respectively. The predicted lateral and rotary photon drag are of order ± 6 × 10 − 8 rad. • Role of dressed sates in view of EIT coherence on the light propagation, optical properties and photon drag. • The nature of dressed states influence largely the optical properties such as group index, group velocity, group delay, and photon drag. • The optimal values of positive and negative group velocity are 6 × 10 11 m/s and − 2.5 × 10 11 m/s, respectively. • The calculated lateral and rotary photon drag are of order ± 6 × 10 − 8 rad.

Experimental, Numerical and Analytical Investigation of the Torsional Vibration Suppression of a Shaft with Multiple Optimal Undamped Absorbers

The aim of the present work is to study the suppressed torsional vibration of shafts, with a clamped boundary condition at either end, via single or multiple undamped absorbers. Structures with such features often suffer from failures (e.g. fatigue, wear) caused by excessive vibrations. The shaft considered is under the action of a harmonic point moment. A vibration design benchmark for torsional absorbers is presented. For both cases of the shaft with one and two absorbers, the variation of absorber parameters, including attaching position, moment of inertia and torsional stiffness, are investigated. The optimal values of the absorber control parameters are obtained. First, the governing equation for the torsional vibration of the shaft and its absorbers is derived in a dimensionless form. Next, the free and forced vibrations of the system are investigated and dimensionless natural frequencies are obtained. To absorb the identified natural frequencies, we compute the $${L}_{2}$$ norm of the angular displacement of the shaft at these frequencies and tune the parameters of the absorbers to minimize the norm. A detailed analytical solution framework for determining the torsional vibration response of a shaft equipped with torsional vibration absorbers is developed. Minimizing the established relations for the $${L}_{2}$$ norm of the shaft’s torsion is examined for a wide range of frequencies, as a criterion for determining its absorption frequency. Advantage of using two absorbers over a single absorber is highlighted. Validation of the analytical model is achieved by comparisons to both numerical and experimental results.

Modeling of Limestone Dissolution for Flue Gas Desulfurization with Novel Implications

Solid-liquid dissolution is a central step in many industrial applications such as pharmaceutical, process engineering, and pollution control. Accurate mathematical models are proposed to improve reactor design and process operations. Analytical methods are significantly beneficial in the case of iterative methods used within experimental investigations. In the present study, a detailed analytical solution for the general case of solid particles dissolving in multiphase chemical reaction systems is presented. In this model, the authors consider a formulation that considers the particles’ shape factor. The general case presented could be utilized within different problems of multiphase flows. These methods could be extended to different cases within the chemical engineering area. Examples are illustrated here in relation to limestone dissolution taking place within the Wet Flue Gas Desulfurization process, where calcium carbonate is dissolving in an acidic environment. The method is the most common used technology to abate SO2 released by fuel combustion. Limestone dissolution plays a major role in the process. Nevertheless, there is a need for improvements in the optimization of the WFGD process for scale-up purposes. The mathematical model has been tested by comparison with experimental data from several mild acidic dissolution assays of sedimentary and metamorphic limestone. We have found that R2 ⊂ 0.92 ± 0.06 from dozens of experiments. This fact verifies the model qualifications in capturing the main drivers of the system.

Relative tracking control of constellation satellites considering inter-satellite link

In this article, two main issues related to the large-scale relative motion of satellites in the constellation are investigated to establish the Inter Satellite Link (ISL) which means the dynamic and control problems. In the section related to dynamic problems, a detailed and effective analytical solution is initially provided for the problem of satellite relative motion considering perturbations. The direct geometric method utilizing spherical coordinates is employed to achieve this solution. The evaluation of simulation shows that the solution obtained from the geometric method calculates the relative motion of the satellite with high accuracy. Thus, the proposed analytical solution will be applicable and effective. In the section related to control problems, the relative tracking control system between two satellites will be designed in order to establish a communication link between the satellites utilizing analytical solution for relative motion of satellites with respect to the reference trajectory. Sliding mode control approach is employed to develop the relative tracking control system for body to body and payload to payload tracking control. Efficiency of sliding mode control approach is compared with PID and LQR controllers. Two types of payload to payload tracking control considering with and without payload degree of freedom are designed and suitable one for practical ISL applications is introduced. Also, Fuzzy controller is utilized to eliminate the control input in the sliding mode controller.

Surrounding gate long channel nanowire MOSFET modelling—extended analysis

Based on the approximate solution of Poisson’s equation in the case of a p-doped silicon body, an improved current-voltage characteristic model of long-channel cylindrical surrounding-gate Si nanowire MOSFET is proposed. The improvement itself considers a realistic description of the carriers’ mobility degradation owing to the radial electric field and a more detailed and accurate analytical solution to the 1D Poisson’s equation than the solutions available in the literature. The model is valid in the wide range of the doping concentration and shows a satisfactory level of agreement with the two-dimensional simulation results and the former models. It can also be applied to different operation regimes such as subthreshold, linear and saturation regimes.

Determination of the Heave and Pitch Motions of a Floating Cylinder by Analytical Solution of its Diffraction Problem and Examination of the Effects of Geometric Parameters on its Dynamics in Regular Waves

In this paper, diffraction problem of a floating vertical circular cylinder is studied. Detailed analytical solution for the boundary value problem to evaluate the wave loads for the cylinder with heave and pitch motions in water of finite depth in the presence of an incident wave, has been presented. Accordingly, diffraction problem for a truncated vertical circular cylinder of radius in water of finite depth has been considered. Incident wave used in this problem, is assumed to be linear with amplitude . In order to calculate the added mass and damping coefficients of the pitch motion of the body, strip theory is applied. For the heave motion, the hydrodynamic coefficients are found by the submerged disk method. Parametric studies of the effects of the wave excitation force on the floating cylinder have been performed for two different cases: 1) constant draft of the cylinder with varying water depth and 2) varying draft of the cylinder with constant water depth.

Analytical and level-set method based numerical study on oil–water smooth/wavy stratified-flow in an inclined plane-channel

Level-set method based transient 2D simulation of developing oil–water smooth-stratified (SS) and wavy-stratified (WS) flow in a horizontal and inclined plane-channel is done; for various inlet-velocity ( u in ), inlet-interface-height ( H in ), inclination-angle ( θ), reduced surface-tension ( σ ⩽ σ ow ) and reduced gravity ( g ⩽ g e ). At the certain critical value of the governing parameters, SS to WS flow transition is captured, analyzed and reasoned. Increase in u in , H in and θ and a decrease in σ ow and g e are found to destabilize the SS flow. For fully-developed SS flow, a detailed analytical solution of interface-height, maximum axial-velocity, its transverse location, pressure-gradient and wall-shear stress is proposed for an inclined channel; an excellent agreement between the present analytical and numerical results is also reported. The SS flow analytical-results are also compared with the time-averaged WS flow numerical-results (near the channel-outlet), to understand the reasons for flow-transition. Flow development is studied with the help of axial variation of interface-height and maximum (over the cross-section of the channel) axial velocity; time-averaged for WS flow. Furthermore, the variation of development-length for SS flow and WS flow is studied. Finally, stretching of interface-area due to onset of WS flow is presented with the help of interfacial-area-concentration. Its calculation directly from the Dirac-delta function of the level set method is a novel-contribution.

Analytical Design, Analysis, and Optimization of Raman Fiber Amplifiers With TDM Pumps

In this paper, we analyze Raman amplifiers (RAs) with time division multiplexed (TDM) pumps via an analytical approach. First of all, a detailed analytical solution for the forward and backward propagating waves in the TDM-pumped RAs is presented. Then, the gain of the TDM-pumped RAs is treated analytically. After revealing the nature of resonant gain enhancement, a relatively simple formula of the optimal input pump power configuration is derived via the least squares method. Afterwards, enhanced double Rayleigh backscattering noise and amplified spontaneous emission noise are analyzed and explicit analytical formulas derived. Thereafter, a simple formula to evaluate the impact of the pump modulation is proposed for the design, analysis, and optimization. The analysis of the TDM-pumped RAs highlights the optimization of the parameters of the TDM pumps, such as the pump wavelengths, pump power, and pump modulation frequency as well as the pumping order.

Analytical description of ascending motion of rockets in the atmosphere

In continuation of a previous work [1], we present an analytic study of ascending vertical motion of a rocket subjected to a quadratic drag for the case where the mass-variation law is a linear function of time. We discuss the detailed analytical solution of the model differential equations in closed form. Examples of application are presented and discussed. This paper is intended for undergraduate physics teachers and for graduate students.

Smith-like predictor for control of parameter-distributed processes

It is demonstrated that, for the best results, the Smith predictor need not necessarily be designed to eliminate time delay of a lumped-parameter process completely from the closed-loop characteristic equation. It is shown how this feature can advantageously be employed in a linear-predictor control of linear parameter-distributed processes containing in their transfer function term exp [-√(as 2 + bs + c)] which cannot be eliminated completely by a physically realizable predictor. Detailed analytical solution of the characteristic equation is given, for a heat-diffusion process compensated by an idealized form of the linear predictor. Digital simulation is then used to demonstrate how a particular rational approximation to this idealized predictor can improve the closed-loop system dynamic behaviour. Both set-point and load step changes are considered.

Analysis of synchronous generator sequential short circuits

A method of analysing sequential short circuits on a synchronous machine is presented, and is applied to the detailed analytical solution for the armature currents following a line-to-line/3-line and a line-to-neutral/3-line-toneutral short circuit. The analysis is carried out in the d, q, o reference frame by a Laplace transform method using the voltages during the unbalanced s.c., which are known from previous analyses. The results show that, following the 3-phase s.c., the currents decay with the same time constants as during a simultaneous 3-phase s.c. together with an additional time constant for the ‘o’ component in the s.c. involving the neutral. The magnitudes of all these components, not just the asymmetrical component as indicated by previous workers, are influenced by the duration and time constants of the unbalanced s.c. As pointed out by previous authors, it is shown that a sequential s.c. can be more severe than a simultaneous s.c., if the duration of the initial s.c. is short compared with the subtransient time constants. The effect of subtransient saliency, which is included in the analysis, is also discussed.

Mixed convection in an isothermally heated horizontal pipe

A theoretical investigation is made into the laminar flow of a large-Prandtl-number fluid through an isothermally heated horizontal pipe. A detailed analytical solution is obtained which shows, in leading approximation, that the fractional bulk-temperature rise is solely a function of (L/aR)(G/P 3) sol1 4 . The theory is found to agree very well with available experimental results and to be a marked improvement over existing empirical correlations.

The motion of shock waves and products of detonation confined between a wall and a rigid piston

In a previous paper, Aziz et al. [1] considered the motion of a rigid piston under the impact of a detonation wave. In their one-dimensional model the back-end of the “pipe” was open, allowing the products of detonation to escape. The present research considers the case when the detonation products cannot escape because the pipe is closed in the rear. The numerical results verify the conjecture that there is a critical value of the mass ratio, r, (ratio of the mass of the undetonated explosive to the piston mass) above which the trajectory of the piston is the same regardless of whether the pipe end is closed or open. A detailed examination of the piston motion indicates an apparent anomaly—the piston speed is increased above the “open-pipe” value before the shock wave rebounding off the closed end reaches the piston again. In order to explain this phenomenon a detailed analytical solution of the piston motion and flow field is carried out, for the case of polytropic detonation products γ = 3.